How to make brick texture straight on dome?
With generated texture coordinates: In the texture tab of the properties panel you can set the mapping of the image texture to Sphere or Tube:

Sphere will cause the texture to be mapped so that the height of the bricks will cover a certain angle. This gives less streching, but the bricks near the top will cover less height. Tube will map it so that the bricks are all the same height, like the bricks should be, but will give you more distortion on the top of the sphere. But for your case tube is probably better.
For comparison: Sphere mapping (left) and Tube mapping (right) of a brick texture on a sphere.



With UV texture coordinates: if you press U to unwrap your object, select "Sphere Projection" to get the effect of the sphere mapping or "Cylinder Projection" to get the effect of Tube mapping. Note however that these mappings depend on the angle of the current view on the object. You should look on the side of the sphere, not on the poles.